Rescaled Whittaker driven stochastic differential equations converge to the additive stochastic heat equation

2018/02/14 by Yu-Ting Chen, Chen, Yu-Ting
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1802.05346

openalex publication_date 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study SDEs arising from limiting fluctuations in a (2+1)-dimensional surface growth model called the Whittaker driven particle system, which is believed to be in the anisotropic Kardar--Parisi--Zhang class. The main result of this paper proves an irrelevance of nonlinearity in the surface growth model in the continuum by weak convergence in a path space; the first instance of this irrelevance is obtained recently for this model in terms of the covariance functions along certain diverging characteristics. With the same limiting scheme, we prove that the derived SDEs converge in distribution to the additive stochastic heat equation in C(\Bbb R₊,\mathcal S'(\Bbb R²)). The proof addresses the solutions as stochastic convolutions where the convolution structures are broken by discretization of the diverging characteristics.

Citations

• Stationary measure of the driven two-dimensional q-Whittaker particle\n system on the torus

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